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Computers and the Mechanics of Communication Read chapter Read first chapter

2015 | OriginalPaper | Chapter

A Note on the Computable Categoricity of \(\ell ^p\) Spaces

Author : Timothy H. McNicholl

Published in: Evolving Computability

Publisher: Springer International Publishing

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Abstract

Suppose that \(p\) is a computable real and that \(p \ge 1\). We show that in both the real and complex case, \(\ell ^p\) is computably categorical if and only if \(p = 2\). The proof uses Lamperti’s characterization of the isometries of Lebesgue spaces of \(\sigma \)-finite measure spaces.

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Metadata
Title
A Note on the Computable Categoricity of Spaces
Author
Timothy H. McNicholl
Copyright Year
2015
Book
Evolving Computability

Print ISBN: 978-3-319-20027-9

Electronic ISBN: 978-3-319-20028-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20028-6_27

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